

A245803


Numerator of the partial sum of the number of prime factors function divided by n.


0



0, 1, 2, 1, 1, 7, 8, 11, 13, 3, 16, 19, 20, 11, 8, 7, 29, 16, 33, 9, 38, 20, 41, 15, 47, 49, 52, 55, 56, 59, 60, 65, 67, 69, 71, 25, 76, 39, 80, 21, 85, 44, 89, 23, 19, 97, 98, 103, 15, 54, 110, 113, 114, 59, 24, 31, 42, 64, 129, 133, 134, 68, 139, 145, 147, 25, 151, 77, 52, 159, 160, 55
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OFFSET

1,3


LINKS

Table of n, a(n) for n=1..72.


FORMULA

a(n) is the numerator of (sum(i = 1 .. n, Omega(i)))/n, where Omega is the number of prime factors function (counted with multiplicity, see A001222).


EXAMPLE

a(8) = 11, since the integers from 1 to 8 have between them a total of 11 prime factors, making our fraction here 11/8.
a(9) = 13, since the integers from 1 to 9 have between them a total of 13 prime factors, making our fraction here 13/9.
a(10) = 3, since the integers from 1 to 10 have between them a total of 15 prime factors, making our fraction here 15/10 = 3/2.


MAPLE

N:= 100: # to get terms a(1) to a(N)
map(numer, zip(`/`, ListTools:PartialSums([seq(numtheory:bigomega(n), n=1..N)]), [$1..N])); # Robert Israel, Aug 29 2014


MATHEMATICA

Numerator[Array[Plus@@Last/@FactorInteger[#!] &, 120, 2]/Range[2, 121]]


PROG

(PARI) lista(nn) = {s = 0; for (n=1, nn, s += bigomega(n); print1(numerator(s/n), ", "); ); } \\ Michel Marcus, Aug 28 2014


CROSSREFS

Cf. A022559.
Sequence in context: A168347 A120475 A086738 * A198941 A058955 A176055
Adjacent sequences: A245800 A245801 A245802 * A245804 A245805 A245806


KEYWORD

nonn,easy,frac


AUTHOR

Alonso del Arte, Aug 22 2014


STATUS

approved



